Within medical science, pattern classification is the basis for computer-aided diagnosis (CAD) systems. CAD systems automatically scan medical image data (e.g., gathered via imaging modalities such as X-Ray, MRI, or Ultrasound) and identify conspicuous structures and sections that may be indicative of a disease. Traditionally, classification is often done using popular methods such as support vector machine (SVM), boosting, and neural networks. These are discriminative approaches since their objective functions are directly related to the classification errors. However, discriminative classifiers are sensitive to data corruption. Their trainings are also prone to over-fitting when facing the lack of training samples.
Recently, sparse representation (SR) based classification has gained significant interests from researchers across different communities such as signal processing, computer vision, and machine learning. This is due to its superior robustness against different types of noise. For example, an SR framework is capable of handling occlusion and corruption by exploiting the property that these artifacts are often sparse in terms of pixel basis. The classification is often done by first learning a good sparse representation for each pattern class. Some examples of effective algorithms for learning sparse representation are the method of optimal direction, KSVD, and online dictionary learning. A test sample is classified by computing maximum likelihood function given each sparse representation. It has been shown that this approach outperforms the state of the art of discriminative methods on many practical applications.
Although SR holds a great promise for CAD applications, they have certain disadvantages that can be improved. In particular, the linear model traditionally employed by SR-based systems is often inadequate to represent nonlinear information associated with the complex underlying physics of medical imaging. For instance, contrast agents and variation of the dose in computed tomography nonlinearly change the appearance of the resulting image. Medical images are also subjected to other common sources of nonlinear variations such as rotation and shape deformation. The traditional sparse representation framework would need much larger number of dictionary atoms to accurately represent these nonlinear effects. This, in turn, requires a larger number of training samples which might be expensive to collect, especially for medial settings.